Calculating apparatus



Feb. 4, '1941. I M. JAKOSKY 2,230,954

CALCULATING APPARATUS Filed June 17, 1940 3 Sheets-Sheet l XYVVAWP '7 l g-6611 0 Feb. 4, 1941.

Filed June 17, 1940 3 Sheets-Sheet 2 v Patented Feb; 4, 1941 .uNiTEo STATES calcumrmo manarcs Milton Jakosk y, Washington, a. 0. Application June 12, 1940. Serial No. 341,041

This invention relates to calculating apparatus.

More particularly, it is concerned with instrumentalities for obtaining the sum of moments with respect to a selected datum point, either within or without the limits of a loaded structure, and for giving as the ultimate answers the center of gravity of such structure under the particular conditionsof loading and the total weight.

The problem to'which this inventionis specifically addressed is that of distributing the disposable portions of the load in an airplane, or other fluid supported craft, so that it shall have safe flight characteristics.

Other similar problems to which the principles of this invention are applicable are both numerous and obvious.

The flight characteristics of an airplane, particularly its longitudinal stability and controllability are dependent principally upon the fore and aft position-of the center of gravity. Since the vertical position of the center of gravity is seldom critical, there is ordinarily no need for taking it into account. However, if the center of gravity'is too far forward, the airplane may be too stable, and there may be diniculty in attaining a tail down position. for landing. On the other hand, if the center of gravity is too far rearward, the airplane may be longitudinally and directionally unstable and there mas be difficulty in attaining a tail high con-- dition essential for takeofi. Consequently, there exist forward and rearward limits for the center of gravity of the airplane, if satisfactory and safe flight characteristics within structural stress limits are to be maintained. V

v The fore and aft center of gravity of an airplane is, of course, adapted by the magnitude and location of the disposable load. In fairly large size aircraft, the disposable load may comprise fuel, oil, crew, baggage, and a number of transverse rows of passenger weights. Also, those aircraft which" incorporate in their design a retractible chassis will have their centers of gravity' changed by extending or retracting the chassis, if a longitudinal shifting of chassis weight is involved.

In order to load an airplane properly, it is obviously essential that its center of gravity for the particular condition of' loading fall within.

50 the approved or limiting fore and aft positions.

Such a calculation in actual practice involves a determination of the moment of each disposable item, the addition of such moments to the moment of the unloaded plane. and division otthemmotthemomentsbythetotal'eight.

If the resultant calculation of the center of gravity position is not within the prescribed limits, a new distribution is assumed and the calcula tion is repeated until a satisfactory position is attained. Thus by trial and error a safe disposition of the load is made. Obviously these calculations are laborious, require appreciable time, and introduce considerable chance of error.

Quite recently, it has been proposed to solve this specific problem by anelaborate compound system of levers which can be loaded to simulate actual conditions. Devices similar to nomographs and slide rules also have been provided for simplifying the required calculations. .I'he first of these proposals entails a very expensive and critical machine for each differentmodel of airplane to be balanced, and'the second, while less expensive does not permit juggling of the load items intermediate acomplete calculation and leaves considerable room for error in the hands of an unskilled or careless operator. Moreover, none is capable of producing a permanent record of a given loading showing the computation for each item of disposable load.

It is an object of the present invention to provide calculating apparatus for algebraically adding in any order a plurality of products, each of which has a constant multiplier, and indicating the quotient of such summation divided by the sum of the respective multiplicands.

A further object is the provision of simple and practical apparatus employing certain Government certification data commonly used for indicating whether or not an airplaneis loaded in accordance with its approved specification.

In the accomplishment of this specific object, a feature of the invention consists in the provision of means for obtaining the center of gravity (longitudinal) of an-aiiplane under particular load conditions and for comparing visually 49 the resultant center of gravity with the prescribed limiting positions for that model airplane.

Another object attained by the invention to be described herein is' the provision of reliable 45 instrumentalities for adding algebraically the m0- ments of the different items of disposable load and dividing that summationby the gross weight at any stage of loading to obtain an intermediate orfinalwesuitant center of gravity.

It is an additional object to provide a load" calculating apparatus for airplanes with means for producing a permanent record of the various load and moment setting 7 More specifically, it is intended to provide an s apparatus oi the character indicated having a plurality of relatively adjustable members or slides in which the slope of each slide edge that is eliective. has a common base line and is chosen to correspond with the moment arm, with respect to a selected datum point, of its load component. Another related feature of improvement is the combination with such members of a pointer or indicating means cooperating with a callbrated chart in order that the intermediate or final result of the load-balancing calculation will be directly readable on the chart and determined by such intermediate or final position of the pointer.

An 'amniiary object resides in the provision of convenient mechanical means for rapidly and accin'ately setting the scale of each relatively adjustable or movable member.

Another object attained by the present invention is the provision of means for making a permanent record of each item of disposable load as represented by the settings or positions of the respective relatively movable members.

Further novel features of improvement contributing to ease and accuracy in operation and mmpliiying construction of apparatus of this nature will be perceived and readily understood from reading the following detailed description of an illustrative embodiment of the invention in connection with the accompanying drawings, in which Fig. l is a plan view in perspective of the complete apparatus;

Fig. 2 is a diagrammatic plan view of the apparatus of Fig. l, and showing a typical calculation in dotted lines;

3 is an enlarged vertical secticnof a slide member actuating means, taken on line AA of Fig. 1;

Fig. e a pian view of a part of the slide member actuating means;

Fig. 5 represents an enlarged horizontal secion taken on the line BB of Fig. 3 to show the slide member actuating means;

Fig. 6 is an enlarged vertical section of a recording device, taken on line G--C of Fig. 1.

Fig. '2 is an enlarged end view of an adjacent pair of slide members and the means for holding them together;

Fig. 8 is a horizontal section taken on line 30-13 of Fig. '2; and 7 Fig. 9 is a vertical section along theline E-E of Fig. 8.

As seen in Figs, 1 and 2, the apparatus comprises a series of horizontal slide members arranged in fan shape for relative linear movement in the same general plane. Slide member I which is fixed and horizontal is graduated in terms of nose cargo. Inclined slide member 2 and 3 are graduated and sloped to give the moment as well as weight of the nose gas and oil loads respectively. Inclined slide member 4 accomplishes the same ior the pilot and copilot. An additional slide member 5 performs the same function for the first row of passengers. Slide member 8 similarly provides for wing gas; and rows 2 and 3 of passengers are provided for by slide members I and 8, respectively. A further slide member 8 is graduated and sloped to subtract the moment and weight eflfect of discharged ballast. In a like manner the added moment and weight effect of rear cargo is taken care of by slide member ll. Vertical slide member H provides means for mechanically determining the difierence in moment produced by longitudinal weight displacement in retracting or extending the chassis. Cooperating with the landing gear scale of slide member H is a vertical slide l2 having a Celluloid covering 13 on its top or scale side. All of the other members or slides are covered in an identical fashion and thus permit the graduations to be made on the Celluloid or similar material. A transparent pointer I4 is carried by the endmost slide member 22.

The preferred thickness for the various slide members is approximately three-eighths of an inch and they may be formed from a suitable plastic, e. g., Bakelite, or from Duralumin or the like. Likewise, the pointer H may be formed from a transparent plastic having intersecting centering lines IE or a similar device at its out ward end for purposes to be described.

Adjustment of the pointer H is provided for by a longitudinal slot l8 extending outwardly from adjacent its inner end and a clamping thumb screw which passes through said slot 18 and is threaded vertically into the end slide,

member 12.

A spaced pair of hinges Z2 and 24 secure the outer edge of member I to a generally rectangular panel board 26 of seasoned wood or other suitable material.

A chart 28, corresponding to a portion of the Government certification data for the particular model airplane and defining as a quadrilateral the fore and aft limits of center of gravity and the range of disposable weight or load, is secured to the panel board 26 in operative relation to the pointer or indicating means H, as shown in Figs. 1 and 2.

The hinge connections 22 and 2! permit raising as a body of the various interlocked slide members and the attached pointer H for the insertion of a suitable record card or sheet 30 in a predetermined position such that the range of movement of each slide member from zero position will be confined to said record card and so that a trace of the set of calculations can quickly and easily be made by running a pencil along the ends of said members after all have been adjusted for the given load conditions.

While in its simplest form the present apparatus needs only to include a series of interrelated, relatively movable slide members, it is highly'desirable that means he provided for quickly and accurately setting'each slide to its required position. For accomplishing the required slide setting, a handknob 32 is disposed between slide members I and 2 adjacent their outer ends. Similar knobs 33 and 34 are likewise positioned between the adjacent edges of slide members 2 and 3, and 3 and 4 respectively.

In a similar manner, knobs 35 and 36 are positioned between slide members 4 and 5 and slide members 5 and t with this particular embodiment and application of the present invention, knobs 31', 38, 39, ll, H and 42 are provided in the required positions between slide members i and-I, I and 8, l and 9, 9 and II, III and II, and ll and I2, respectively.

Since all of these knobs and their relation to adjacent slide members are the same, it will be suflicient to describe in detail knob 32 which is positioned between members I and 2. Referring to Fig. 3, attention is called to the hollow shaft II which extends below the knob proper and terminates in a horizontal pinion gear 1 which may be integral therewith. Ordinarily, these be formed of a suitable metal.

The knob 32 and its gear are supported by the slide 1 so as to engage a rack section ll which is fixed to slide 2. The rack ll in each instance will be of such a length and so positioned as to accommodate the required relative movement of this particular pair of slides.

, An opposed pair of horizontal T-grooves i and 52 are formed in the edges of members I andl, respectively, to provide an H-shaped housing for the gear 46 and rack 48. On their meeting faces the members i and 2 mayalso be provided with a tongue and groove pair 53 for maintaining vertical alignment. In addition, a horizontal recess 54 of semicircular shape extends from the groove or slot 50 to accommodate the gear I in member i. There is also a vertical slot 55 extending downwardly from the upper side of member 1 to permit lateral insertion of the hollow shaft ll of knob 32. A cover plate 5 is countersunk below the lower face of member l and has an upwardly projecting stud portion 5'! fitting closely in shaft 44 and retained by a stud engage the slide member l.

In Fig. 6, there is illustrated a single recording perforator 64, one of which is positioned close to the inner end of each slide member. Each perforator GE is pointed at its lower end and arranged to slide vertically in a bore 85, having a guiding sleeve 66, through its slide member. To hold said pointed perforator G4 in a retracted position, a thin spring strip $8 loosely engages its upper end beneath a finger knob 65, in the manner shown, and has its opposite end secured to l by a locking pin an and a locking and anchoring pin 82 respectively. It is preferable that the sliding bearing plate 16 be somewhat longer than the stationary plate 18; seeg'Fig. 8. The

locking pin or machine screw 82 is anchored in' the slide member 2 by its cooperation with an upwardly extending bore 84 thereof. One or more of the holding means I2 may be used between each pair of slide members to draw them together, and anchored to the slide member of the pair which moves relatively of the other in setting.

It is believed that the operation of the apparatus which has been set forth-in detail above can be most readily understood by a consideration of its application to a specific problem in load balancing as exemplified by thedotted line positions of the slide members and pointer shown in Fig. 2.

On the chart 28, the ordinate distances represent moments (inch-pounds) or moments abbreviated to index numbers. The horizontal or abscissae distances are measures of weight (pounds). Therefore, the ratio of moment (M) to weight (W) determines the lever arm (R) for a particular condition of moment and weight. If from this particular condition the weight and moment factors are increased or decreased in such a manner as to maintain a constant ratio, the locus will be a straight line.

Accordingly, the upper linear' limit of the quadrilateral diagram of chart 28 defines the aft limit to which the center of gravity, 0. g., of the airplane can be shifted longitudinally without exceeding the approved fore and aft center of gravity limits of the airplane, and the lower linear limit, the forward limit for such displacement as the airplane is loaded.

The empty weight will establish the extreme left positionof the certification diagram with respect to the axes of chart 28; and the opposite or extreme right boundary of the diagram is deby the permissible gross weight of the loaded airplane, that is, the empty weight addedto the disposable load weight.

The possibility of confusion in making the required settings is reduced if a datum plane is selected which will result in all moments being of the same sign, that is, each item of weight will tend to produce rotation in the same direc tion with respect to that datum. Accordingly, the datum hereinafter employed is that passing through the centroid of nose cargo of the craft.

Obviously, appropriate rearrangement of the relative angular slopes of the slide members and a corresponding relocation of the datum will per- I mit the calculator of the present invention to he used in other quadrants and in a range of several quadrants, as exigencies of the problem may entail. Any desired change in the number of variables dealt with in the calculation can likewise be made.

Referring now to Fig. 2, the centering lines 16 of the adjustable pointer M will be set initially on the left of chart 28 in a position corresponding to the weight empty and c. g. of the airplane before addition of the disposable items of load, and the slide members will be concurrently zeroed to the pattern of the full line showing. While it has been stated previously that the settings for'the calculation may be made in any order, they will now be described in their position sequence.

The nose cargo is at the selected datum, and, therefore, the movement of the index arrow on slide member 2 relative to that scale of fixed member I will be horizontal-to add weight, as indicated by pointer l4, without increasing the total moment. In the dotted line position the setting is for 200 lbs.

As slide member 3 is moved relative to member 2 to a position representing the addition of 50 gal. of nose gas, all of the interlocked slide members to the left thereof will move in a manner which will add moment as well as weight to the intermediate position of pointer I4. Attention is called in particular to the fact that the slope of the inclined, linear path of the pointer I 4 during this setting is that determined by the measured lever arm of the nose gas load. In other words, increase in moment has a linear variation with increase in weight. That is, of course, true of each of the inclined slide members remaining to be described.

The effect of "oil" load is introduced into the calculation by means of the inclined scale on slide member 3 upon which is set to 16 gal. the index arrow carried by slide member 4.

So, the pilot-co-pilot scale on the upperfor wing gas is the same as for passengers row 5, Accordingly, the wing gas" scale of slide member 6 is made parallel with passengers row 1 scale of slide member 5, and the former cooperates with an index arrow carried by slide" member i to register 100 gal.

The upper edge of slide member I is marked with a passengers row 2 scale, with respect to which an index arrow on slide member 8 is appropriately moved for a load condition of one passenger.

For passengers row 3, there is a scale on the upper edge of slide member 8 cooperating with an index arrow on slide member 5, and the setting here is also for one passenger.

Ordinarily, the removable ballast will be reduced or completely discharged as suihcient disposable load is taken on, and that condition is met by the reverse or inward movement of the index arrow on slide member ID with respect to the ballast" scale on slide member 8, as the former is set to its dotted line position. The.

pointer M, will, therefore, be moved backward appropriately to subtract 170 lbs. of ballast weight and its moment from the mechanical calculation. The empty weight of the airplanein the present case included 340 lbs. of ballast.

Slide member ID has on its inclined upper edge a scale graduated in terms of "rear cargo" and the index arrow on slide member ii I for that scale is set to a load of lbs.

In this particular airplane operation of the main landing gear is accompanied by a longitudinal shifting of its centroid or variation of its lever arm. By means of an up" and down vertical scale on slide member H cooperating with an index arrow on pointer slide member I 2, the variation in moment without addition of weight can be properly included in the bdancing calculation. Since the centroidof the chassis is moved away from the datum in the up position, this will be another addition in moment, as shown dotted. Through algebraic addition of moment items and addition of weight or moment alone, the calculation has been taken through the required steps to produce a 'final (and-dotted) pointer H position which falls within the safe limits defined by the quadrilateral diagram of chart 28. VlTrth the suitable intermediate c. g. position lines which are provided that diagram, the resultant c. g. position as well asthe gross weight are readable directly. v

If desired, a permanent record or load manifest can now be made by perforating the record card or sheet 30 by means of the recording means or perforators $4 with which each slide member is provided adjacent its inner end to show final relative positions, it being noted that the hinged member I which is fixed as regards relative movement in the plane of the card 3| also carries 9.

perforator 64 in order that an orienting point can be produced on said record card. A pencil trace may also be made along the ends of slides by way of a further or alternative record of the balancing calculation.

By way of summary, it is observed that the slope of each slide member scale represents a definite moment arm or constant multiplier, and that each scale represents a variable load in pounds (multiplicand), although in some instances the graduation is, for convenience, in terms of volumetric or other load units.

The mathematical capacity of the apparatus of this invention may be represented by the following exprsslon which will be subsequently defined:

Q represents the quotient of the indicated division of numerator by denominator.

Fineachinstanceisavariablehavingany value from zero (0) to the physical limits of a particular apparatus. The variation is not necessarily a linear one since the scale graduations can be made correspondingly non-uniform.

L is representative of a single constant factor or multiplier and determines the slope of one scale edge of a. particular slide member.

V stands for the magnitude in a vertical axis direction of any PL product which is to be added or subtracted initially or finally to the other part of the numerator in the above equation.

H similarly represents an F magnitude in a. horizontal axis direction to be added or subtracted initially or finally to the other part of the denominator in the above equation.

Vand Heap. bezeroor anyrealvalue, subject only to the physical limits of the apparatus.

As used in the specification and claims, slide", "member", and slide member" refer to the same elements which have been illustrated specifically; andthese as well as all other terms which havebeenusedaretobetakenlntheirillustmtive rather than limiting sense.

It is contemplated that the sets of slide members comprising the kinetic parts of the calculating apparatus will be supplied separately as articles of manufacture, and for that reason certain of the appended claims have been drawn to such a sub-combination.

Having thus described the invention, what is claimed as new and desired to be secured by Letters Patent is:

1. In a calculating apparatus of the character described, a plurality of adjacent, lnterlocbd members constructed and arranged to slide linearly relative to each other in the same gmeral plane, the member at one end being adaptedtobefixedinpositionduringacalculaflng operation, and the member at the other end having indicating means movable therewith for cooperation with a. chart, and each member having at least one edge sloped with respect to a common base line according to the relative value of a fixed multiplier, and the said edges ofthemnbers beingvariously sloped, wherebyat each membersettingtheindicatingmeanswillbegivm a movement having the direction of the slope ofthe member edge immediately adjacent themcm- .berbeirgsetandwithmswthwhichitisrfl of each member setting will be given a movement having the direction of the slope of the member edge immediately adjacent that member, and with respect to which it is relatively moved in making that setting, and the movement of the pointer having a magnitude representing a given multiplicand; and perforating means on each member for recording its relative position.

3. In a calculating apparatus of the character described, a plurality of adjacent, interlocked members provided with cooperating scale and index means on their adjacent edges and constructed and arranged to slide relative to each other in a single plane, the member at one'end being adapted to be anchored in position; an adjustable pointer carried by the member at the other end, and each member having at least one edge sloped with respect to a common base line to correspond to a fixed factor, and'the said edges of the members being variously sloped, whereby at each member setting the pointer will be given a movement having the direction of the slope of the member edge immediately adjacent the member which is being set, and with respect to which it is moved in setting, and a magnitude representing a. given multiplicand; and means for setting said members.

4. In a calculating apparatus of the character described, a plurality of adjacent members constructed and arranged to be moved relative to each other, the member at one end being adapted to be anchored in position; a pointer carried by the member at the other end, and each member having at least one edge sloped with respect to" a common base line to correspond to a fixed multiplier, and the said edges of the members being variously sloped, whereby at each member setting the pointer will be given a movement having the direction of the slope of the member edge immediately adjacent the member which is being set, and with respect to which it is moved in setting, and a magnitude representing a given multiplicand; means for setting said members;

and resilient means for drawing said members together in a common plane, the setting means and holding means being adapted to cause the pointer-carrying member and all members between it and the edges of relative movement tomove together. I

- 5. Calculating apparatus for algebraically adding in any order a plurality of products, each of which has a constant multiplier, and indicat ing the quotient of such summation divided by the sum of the respective multiplicands comprising, in combination, an interlocked series of relatively movable co-planar members including a fixable member at one end of the series; a pointer secured to the member positioned at the other end of the series, each of the intermediate members having opposite edges sloped with respect to a common base line and matching with. the meeting edges of the adjacent members, and. each of the end members having its inner edge sloped. in a similar manner with respect to the common baseline, and matching the meetin each member for recording the relative positions of the various members. I

6. Calculating apparatus for algebraically adding in any order a plurality of products, each of which has a constant multiplier, and indicating the quotient of such summation divided by the sum of the respective multiplicands comprising, in combination, an interlocked series oi] relatively movable members with cooperating scale graduations and indexes and including a fixed member at one end of the series; a pointer secured to the member positioned at the other end of the series, each of the intermediate members having opposite edges sloped with respect to acommon base line and with the meeting edges of the adjacent members, and

each of the end members having its inner edge I sloped in a similar manner with respect to the common base line, andmatching the meeting edge of the adjacent intermediate member, and the said edges of the members being variously sloped whereby setting of any movable member will impart to the pointer a resultant movement which has as its components the horizontal and vertical movement corresponding to the slope of the member edge directing that setting and the magnitude 'of movement along that member;

and a chart diagrammed according to preselected limits arranged for cooperation with said pointer in its range of movement, whereby the position at-any time of the pointer, with respect to said chart,'will determine conformity to said limits.

7. Calculating apparatus for algebraically adding in any order a plurality of products, each of which has a constant multiplier, and indicat ing the quotient of such summation divided by the sum of the respective multiplicands comprising, in combination, an interlocked series of relatively movable members includinga fixed membet at one end of the series; a pointer adjustably secured to the member positioned at the other end of the series, each of the intermediate members having opposite edges sloped with respect to .magnitude of movement along that member; a

diagrammed chart arranged beneath the pointer and marked with certain limits; and means on' each member for recording the relative positions of the members at the completion of the cal culation.

8. In a calculating apparatus for balancing the load of an airplane or the like comprising,

in combination, an interlocked series or members relatively movable with respect to each other in which the member at one'end of the series is adapted to be fixed, and the member at the other end of said series being provided with indicat ing means for cooperation with a chart, and each of the intermediate members of the series having predetermined slopes on its opposite edges which coincide with those of the adjacent edges respectively of the other members, the slope of each such edge being referred to a common base line and corresponding to the moment arm of an item of disposable load, and the members having cooperating scale graduations and index means for facilitating the respective settings.

9. In a calculating apparatus for balancing the load of an airplane or the like comprising, in combination, a coplanar, fan-shaped-series of interrelated members relatively slidable with respect to each other in which the member at one end of the series is adapted to be fixed, and indicating means movable with the member at the other end of said series and arranged for cooperation with a chart or the like, each of the intermediate members of the series having predetermined slopes on its opposite edges which coincide with those of the adjacent edges respectively of the other members, the slope of each such edge corresponding to the moment arm of an item of disposable load, and the members having cooperating scale graduations and index means for facilitating the respective settings, said scale graduations being representative of load in units of weight, whereby the position of the indicating means will serve to indicate the displacement of the center of gravity of the airplane or the like as disposable load is added or subtracted.

10. In a calculating apparatus for balancing the load of an airplane or the like comprising, in combination, a. coplanar series of interlocked members relatively movable with respect to each other and in which the member at one end of the series is fixed; a pointer carried by the member at the other end of said series, each of the intermediate members of the series having predetermined slopes on its opposite edges which coincide with those of the adjacent edges respectively of the adjacent members, the slope of each such edge being referred to a common base line and corresponding to the moment arm of an item of disposable load, and the members having cooperating scale graduations and index means for facilitating the respective settings, said scale graduations being representative 01' load in units of weight; a chart cooperatively disposed with respect to the pointer and indicating prescribed limits for disposable load and longitudinal displacement of the center of gravity of the airplane or the like; and means on each member for recording the final relative position of each member.

11. In a calculating apparatus of the character described, a panel board; a plurality of'adjacent members constructed and arranged to be moved relative to each other in a plane parallel to that of the board, the member at one end being hingedly connected adjacent its outer edge to the panel board; a pointer carried by the member at the other end, and each member having at least one edge sloped with respect to a common base line to correspond to a fixed multiplier, and the said edges of the member being variously sloped, whereby at each member setting, the pointer will be given a movement having the direction of the slope of the member edge immediately adjacent the member which is being set, and with respect to which it is moved in and a magnitude representing a given multiplicand; means for setting said members; resilient means for drawing said members together in a common plane, the setting means and holding means being adapted to cause the pointercarrying member and all members between it and the edges of relative movement to move together; a chart arranged beneath the path 0! the pointer; and means on each member for recording the relative positions of the members at the com pletion of the calculation.

MILTON Jjixosxr. 

